Hartree-Fock Theology – Part 1

How a quantum mechanics course laid a new foundation for my faith.

I attended the ‘advanced quantum mechanics’ course 2014 at ETH Zürich in Switzerland. It was taught by professor G.M. Graf in the spring semester. In one lecture, we discussed the so-called Hartree-Fock method which can be used to find approximate solutions for the wave function of atoms, i.e. the distribution of electrons around the atom. The method starts by assuming that a suitable solution has a specific form F. In the next step, we come up with an initial guess that satisfies form F. After that, the laws of physics govern a procedure in which the initial guess is iteratively transformed into a solution X. The solution X describes where the electrons that surround the atom’s nucleus are most likely to be found. Is it guaranteed that X is the correct solution? No, because our initial assumption of form F might be wrong. Or maybe the physics that governs the problem is a bad approximation of reality. However, if we get the physics right, the method ensures that we only find solutions X that could - in principle - be true solutions. Self-contradictory solutions do not appear as candidates.

Learning about the Hartree-Fock method was a revealing moment to me. I realized that even though the (precise) solution for a problem might be unknown, we can identify some potential candidates for the true answer from the sea of all possible answers. Being always personally intrigued by how things really are, I explored how the principles of the Hartree-Fock method could be applied elsewhere. Namely, in the notoriously subjective field of Worldviews. While they are subjective by definition for each person, similar worldviews are shared by sometimes large communities of billions in the case of world religions. And as we all know too well, worldviews are not just a mere epiphenomenon. They dramatically influence people’s behaviors, sometimes at the crossroad of death and life. I was attracted by the idea that some objectivity might be brought into this very subjective business. To me, this endeavor is to be understood very much as a critical self-assessment of my own beliefs and assumptions about the world rather than an external verdict about the worldviews of others.

In analogy to the Hartree-Fock method, the solution we want to find is the worldview. But what is the counterpart to the laws of physics that govern the behavior of electrons? What could act as a force on a worldview that would result in an iterative process that transforms a worldview? Because all of us have their own worldview as a set of basic beliefs and corollaries thereof in their head, we are the ones that change how we see the world and what we believe about it. This means that we are the point where the forces interact with the worldview, but what are the forces? I propose that all influences on a worldview may be divided into three categories or dimensions. Each dimension exhibits its individual characteristics and is governed by its own laws. The following describes the three dimensions and illustrates how the iterative process could look like.

1. Science. This may be the most obvious and natural one. The physical reality we live in is a fact we cannot deny; the laws of nature are an inevitable boundary condition to anything we do in our world. Therefore, every worldview that wants to be a good candidate should embrace physical reality. My current worldview can serve as a natural starting point for the iterative process. If my worldview contains beliefs that contradict science, the laws of nature serve as the force of change to my worldview.

For example, if I believe that murmuring a spell allows me to defy gravity and I jump off the springboard at the pool to test it, reality gently reminds me of a conflicting belief. Some belief systems are hard to test this way because they come up with a long list of reasons why it didn’t work in this case. As I will discuss later, this is not necessarily an indication of a bad worldview but it’s definitely a warning sign. Some beliefs are naturally much harder to test for consistency with science than others. We might not even encounter those situations that would reveal a possible conflict. Larger communities with a common worldview can benefit from a wider range of experiences that test it. However, this transferability of knowledge must be carefully discussed because of the subjective and individual component of worldviews. What I believe is slightly different than what other members of my community believe, I have a different body and my neurons are connected in a different way. This leads to the second dimension.

2.The subjective reality. We all are the centers of our universes. While the sciences are objectively and empirically true, my perception of reality is – by definition – subjective.

I am part of the world and what I believe about the outside world must be compatible with my inside world. Insights from psychology suggest that we weigh emotions much more than facts. During discussions, people usually have a feeling first and later provide facts that support it. People dominantly believe what makes sense to them irrespective of scientific support. Science-skepticism and anti-vaxxer tendencies are good examples. Notwithstanding the robust scientific evidence for the efficacy and safety of vaccines, many people do not trust it and don’t get the vaccine. They adhere to their worldview rather than to what scientists tell. During the coronavirus pandemic, social distancing rules were reluctantly imposed. They did not feel right to many - despite their scientifically proved efficacy. When it comes to conflict between outside and inside reality, outside reality has a difficult standing. This illustrates well, that we only adopt or maintain a worldview that makes sense to us personally. It must “feel right”. Conflicts between a worldview and subjective reality can be more subtle. Many worldviews contain the concept of good and bad. If my worldview tells me that prayer should make me feel good but I always feel bad, I have a worldview that conflicts with my subjective reality. We must be careful to not jump to conclusions too fast. Emotions are (learned) reactions to specific situations. There is no guarantee that my feelings were appropriately trained. They probably mostly aren’t. Nevertheless, we strive for coherence between our inner and outer world which should be reflected by the worldview. We can tolerate a dissonance between our inner and outer world if it feels right within the framework of the worldview. The iterative process in this dimension results in a mutual adaptation of feelings and beliefs until a sufficient level of coherence is reached. Being a scientist myself, I am tempted to impose transferability. A good worldview must be sufficiently general such that it could, in principle, be held by anyone without creating a conflict in the subjective reality.

3. Philosophy. The third dimension is the least obvious. People are naturally very good at combining inconsistent beliefs. It takes us less effort to live with a contradiction in our set of assumptions. The looser and the more indirect the connection, the easier we can tolerate a discrepancy between two beliefs. However, philosophy constitutes the same tool for the spiritual realm as is empiricism for the physical reality. The instruments of Philosophy allow us to examine intellectual constructs and beliefs. It teaches us how to properly reason. I think of the naturalistic fallacy, the problem of induction or the category mistake. Logic is of course one of the most fundamental ones. A good worldview must not conflict with this part of reality either. A prominent example is ethics. Ethic withdraws itself from scientific means in the strictest sense (c.f. naturalistic fallacy). An equation or a law of nature is not ethical. Nevertheless, ethics is of fundamental importance for us. It is all too tempting to construct an ethic from nature but then we would give in to the naturalistic fallacy.

We naturally discuss topics that are closest to us. But for something as general as a worldview, everything that exists must find its place in it, also those things far away. I appreciate the philosophical discussion of beauty, love, constitutions, democracies, and consciousness. These are just some of the problems I am aware of that exist. There is a wealth of philosophical problems I am not even aware exist. But my worldview must have a proper acknowledgment, appreciation, and space for them and must agree with insights from philosophy about the spiritual realm.

We have established the three dimensions that constitute the driving forces in the iterative process: 1. science, 2. the subjective reality, and 3. Philosophy. In order to start the iterative process, we need an initial guess that satisfies some conditions. What are these conditions? I will argue in the next post “Hartree-Fock Theology – Part 2” that self-consistency and adherence to Ockham’s razor are two preconditions that should be satisfied by any initial guess.